Teaching sin and cosine instrument

ABSTRACT

A device that teaches the relationship between a right triangle, the length of its hypotenuse, the length of its two sides and the trigonometric functions. The device includes a horizontal and vertical ruler attached by a sliding attachment bracket. A circular plate showing 360 degrees (θ) is attached to the horizontal ruler along with a pivoting ruler that can rotate 360 degrees. By sliding the vertical ruler along the horizontal ruler and revolving the pivoting ruler, the height of the vertical ruler (Y) where it intersects the pivoting ruler, the length of the horizontal ruler (X) where it intersects the vertical ruler, and the length of the of the pivoting ruler (R) where it intersects the vertical ruler can be measured. The trigonometric functions can then be calculated and plotted by their relationship with the measured values of X, Y, R and θ.

BACKGROUND OF INVENTION

1) Field of the Invention

The invention relates to devices, which provides a teaching method forgeometric concepts relating to a right triangle and the relationshipsthat exist between its hypotenuse (R), the length of its two sides (Xand Y) and the trigonometric functions.

Across the nation, schools are going through a major reform in theirmath and science curriculum to bring education standards up to par. Thefacts show that there is an achievement gap between blacks and whites inmathematics and science. In 1999, when the latest National Assessment ofEducation Progress (NAEP) test was administered, large differencesremained between average scores for blacks and Hispanics on the onehand, versus whites and Asians on the other. Nationally, the achievementgap did not narrow at all during the 1990s. In reading and math, gapsseparating poor and minority students from others actually widened atmost grade levels and remained the same or dropped only slightly atothers (The Education Trust). By the end of grade 4, African American,Latino and poor students of all races are already about two years behindother students. By the time they reach grade 8, they are about threeyears behind. By the time they reach grade 12, if they do so at all,minority students are about four years behind other young people. Themathematics and science skills of 17-year-old African American andLatino students are similar to those of 13-year-old white students.African Americans and Latinos obtain college degrees at only half therate of white students. The partnerships between government agency,industry, academia and private organizations are trying to address theseissues along with many others. This invention provides a method forteaching the geometric concepts of a right triangle and trigonometricfunctions.

2) Prior Art

The prior art consist of teaching the theory and equations for thegeometry of a right triangle, its sides, angles and the relationshipbetween the trigonometric functions. Lessons primarily consist ofmathematical explanations and graphs of the trigonometric functions.Equations such as Y=R sin θ or X=R cosine θ along with othertrigonometric functions can be graphed and thus generate the resultingcurves for each function.

The present invention, as distinguished from the prior art, provides adevice that clearly demonstrates the relationship between a righttriangle, its sides, angles, and trigonometric function. None of theprior art uses a device or tool that includes a horizontal and verticalruler attached by a sliding attachment bracket along with a circularplate showing 360 degrees of the circle attached to the horizontal ruleralong with a pivoting ruler that can rotate 360 degrees around thecircular plate.

SUMMARY OF INVENTION

The present invention is designed to teach the relationship between aright triangle, the length of its hypotenuse (R), the length of its twosides (X and Y) and the trigonometric functions.

One of the objectives of the present invention is to provide a devicethat will bring the level of learning and understanding of a righttriangle and the trigonometric function to a conceptual level ratherthan just a fact remembering level as described in the Blooms Taxonomy.

Another objective is to clearly show how the cosine function is relatedto X/R, (the x axis/the hypotenuse).

Another objective is to clearly show how the sine function is related toY/R, (the y axis/the hypotenuse).

Another objective is to clearly show the remaining trigonometricfunctions (tangent, cotangent, secant, and cosecant) and their ratios toX, Y or R as defined for the sine and cosine functions above.

Another objective is to use the invention to generate graphs of thetrigonometric function using data collected from measurements of thelengths of the rulers at their intersections and the angle.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is an off angled view of the invention.

FIG. 2 is a front view of the invention.

DETAILED DESCRIPTION

The present invention is designed to teach the relationship between aright triangle, the length of its hypotenuse (R), the length of its twosides (X and Y) and the trigonometric functions.

Referring to FIG. 1, the device includes a horizontal ruler (X) andvertical ruler (Y) attached by a sliding attachment bracket. A circularplate showing 360 degrees of the circle is attached to the horizontalruler along with a pivoting ruler (R) that can rotate 360 degrees aroundthe circular plate. By sliding the vertical ruler to different positionsalong the horizontal ruler and revolving the pivoting ruler to differentangles (θ), the height of the vertical ruler where it intersects thepivoting ruler, the length of the of the horizontal ruler where itintersects the vertical ruler, and the length of the pivoting rulerwhere it intersects the vertical ruler can be measured. Thetrigonometric functions can then be calculated by their relationshipwith the measured values of X, Y, R and θ. For example, sin θ=Y/R andcosine θ=X/R. The sin and cosine functions and other trigonometricfunctions can be calculated and plotted (e.g. θ vs. Y/R) by varying theposition of the rulers with respect to each other.

Classroom activities can be developed using the present invention thatwill increase the level of understanding of the trigonometric functions.One such activity involves leaving the pivoting ruler at a constantangle (e.g. 30 degrees). Slide the vertical ruler to different positionsalong the horizontal ruler. This allows the right triangle that isformed by the pivoting ruler, the vertical ruler and the horizontalruler to change in size while keeping the length of each rulerproportional to each other. Measure the length of the pivoting ruler(R), the horizontal ruler (X) and the vertical rulers (Y) for eachposition that the vertical ruler is moved to on the horizontal ruler.Calculate the ratio of X/R and Y/R for the different positions. Rememberthat the angle is kept constant. Students will find that the ratios X/Rand Y/R will also remain constant even though the vertical ruler ismoved to different positions on the horizontal ruler. The students learnthat the cosine θ (X/R) and the sin θ (Y/R) will remain constant as longas the proportions of the right triangle are the same. The same methodcan be used for the other trigonometric functions. The present inventionallows a more comprehensive understanding of the concepts of thetrigonometric functions.

Another classroom activity involves moving the pivoting ruler todifferent angles. For example, starting at 0 degrees, move the pivotingruler to different angles at increments of 15 degrees. The pivotingruler can move all the way around the circle 360 degrees. Move thevertical ruler so that it is always intercepting the pivoting ruler.Measure the lengths of the rulers (X, Y, and R) for each angle θ. Whenthe pivoting ruler is in the first quadrant, X and Y will have positivevalues. When the pivoting ruler is in the second quadrant, X will have anegative value and Y will have a positive value. When the pivoting ruleris in the third quadrant, X and Y will have negative values. When thepivoting ruler is in the fourth quadrant, X will have a positive valueand Y will have a negative value. R will always have a positive value nomatter what quadrant the pivoting ruler is in. And it doesn't matter howbig the triangle is as was learned in the previous activity because theratio will stay constant for a given θ. Calculate the values for X/R andY/R for each angle θ. Make a plot of θ vs. X/R and θ vs. Y/R. X/R andY/R will be located on the y axis and θ will be on the x axis. Theresults of the plots will be the cosine curve and the sin curve.Participating in this activity with the present invention allows a morecomprehensive understanding of the concepts of the trigonometricfunctions.

1. A device including a horizontal ruler (length X) and vertical ruler (length Y) attached by a sliding attachment bracket, a circular plate showing 360 degrees (angle θ) of the circle attached to the horizontal ruler along with a pivoting ruler (length R) that can rotate 360 degrees around the circular plate.
 2. A device of claim 1, wherein the A pivoting ruler revolves to different angles (θ), and measures the height of the vertical ruler (Y) where they intersect.
 3. A device of claim 1, wherein the vertical ruler slides along the horizontal ruler, and measures the length of the horizontal ruler (X) where they intersect.
 4. A device of claim 1, wherein the vertical ruler intersects the pivoting ruler and measures the length of the pivoting ruler (R).
 5. A device of claim 1, wherein the vertical ruler, the horizontal ruler and the pivoting ruler can be positioned to form a right triangle in any of the four quadrants and used to measured values of X, Y, R and θ to determine values of the trigonometric functions.
 6. A device of claim 1, wherein the device allows data to be collected that can be used to plot the curves of the trigonometric functions.
 7. A device of claim 1, wherein the vertical ruler (Y) has marked off units consisting of one section with positive numbers and the remaining section with negative numbers.
 8. A device of claim 1, wherein the horizontal ruler (X) has marked off units consisting of one section with positive numbers and the remaining section with negative numbers. 